Refinements in the nonlinear term of a turbulence predictive model based on atmospheric surface layer observations

The recently proposed near-wall turbulence predictive model quantifies the degree of the superposition and the amplitude modulation exerted by large-scale coherent structures on small scales in the linear and nonlinear terms of the formula, respectively, and achieves the prediction of streamwise velocity in the inner region. However, the multiscale effect and the time shift confirmed in the amplitude modulation have not yet been simultaneously taken into account in the model, which could limit the prediction accuracy especially at high Reynolds numbers. In this study, the role of the nonlinear term in the model is clarified based on high-quality flow data obtained in atmospheric surface layers: it redistributes the energy of the universal signal in the time domain and determines the accuracy of the predictive odd moments. An analysis of the multiscale effect and the time shifts in the nonlinear term is subsequently conducted, followed by a demonstration of the refinement in the quality of the universal signal after separately incorporating them into the model. The amplitude modulation is revealed when the two factors are simultaneously considered, and profiles of the scales that dominate the modulation and time shifts with height is provided. Thus, the nonlinear term of the existing model is modified, proposing an polished scheme that can quantify the nonlinear modulation terms more accurately.